Dapthar

I, and countless other posters in the Mathematics forums would greatly appreciate it if there were a "Wrap [math] tags around selected text" button in the Message Editor Interface window, similar to those for the "Bubble" and "bold" tags, for it would allow equations to be typed much more easily. Thanks, Dapthar

I wouldn't consider myself a Mathematician as of yet, but simply a student of Mathematics. IRT: My only formal musical experience was learning to play the piano for a introductory music class (for a University liberal arts requirement), and my "skill" was nothing more than practice and rote memorization, to a level which was sufficient to earn a good grade. As soon as I left the class, I forgot essentially everything I learned in it, to the point where now, only a year later, I cannot read sheet music, or even remember basic finger positions. However, this may be due, in part, to the fact that I didn't have any non-academic desire to learn to play in the first place. Not much more beyond the basic level that relates all endeavors to Mathematics, since, in my opinion, knowledge of anything beyond basic Mathematics doesn't help to improve one's musical talents to any significant degree. Sure, there is the subfield of Music Theory, however, from a Mathematical standpoint, it could be called "Sound Theory" with no theoretical changes to the established literature.

1. True.2. They still are undefined at the University level, and beyond. 3. True.

The only way I see this happening is if you count the total number of students a professor lectures to in one semester, and if the professor is covering several different introductory lectures. In my experience, the largest lectures I have attended had a maximum of 300 students, and those were introductory classes, like first year Physics, Computer Science, and EE courses. After the first year, the lecture sizes drastically drop, and by the time one gets to their final (undergraduate) year, about 30 students is the most one will see in a class.

I believe the first part about being a student at Manchester University might have had a larger impact than the IQ test results. I wouldn't think that they hold credence in matters of any measurable import. Unless there is some sort of standardization' date=' e.g. all potential applicants take the same version of an IQ test, there is no objective way to judge what bearing IQ has on a candidate's potential success. I wouldn't worry about it. I belive they lost their status (In the US, anyways) as a valid testing tool after the attempt to use IQ tests to justify institutionalized racism (See below). I'm sure you'll have a fun time going up to people, and asking them "Mind if I feel your intelligence?".

If by begin, you mean start learning about the material in question, then I'm sorry to say that http://mathworld.wolfram.com/ is more of a technical reference rather than a tutorial site. You'd be better off finding a combinatorics textbook than trying to learn specific topics from that site.

Anyone else see the problem with this statement, or is it just me? paganinio, you realize that if your assertion was true, there would be no point in attending any post secondary institution, correct? Care to explain how this is possible? Sayonara³: It's kind of sad that you had to explain the poll, to someone who has supposedly reaped some of the benefits of post secondary education, no less.

It's used in Quantum Mechanics and other areas of Physics. Suggested reading: http://www.du.edu/~jcalvert/phys/groups.htm. The linked article outlines some of the applications of group theory in Physics. If you already are familiar with group theory, then you'll probably want to read only the first 3 paragraphs, and the sections "Applications to Quantum Mechanics", "Continuous Groups", and "Conclusion", for the rest of the article is a basic introduction to group theory. Also, there is also a book that discusses the applications of Group Theory in Physics, entitled Group Theory and Physics, link: http://www.amazon.com/exec/obidos/tg/detail/-/0521558859/102-7909745-4660944?v=glance.

I think it would be nice if the recent topics on the main page were "unbolded" after they were viewed by the user, like they were before the home page was revamped.

Introductory (i.e. undergraduate) Real Analysis courses will generally introduce the concept of metric spaces. Introductory Topology courses will usually cover them in much greater detail. It's called by the same name in the US, but is usually abbreviated M.S.

Sure. The "bar notation", as I call it, indicates that the sequence under the bar repeats forever, like [math]1/3=.\overline{3}[/math] or [math]1/7=.\overline_{142857}[/math]. So, technically, writing [math]0.\overline{0}1[/math] is meaningless, since one cannot write something after the zeros. The whole point of writing [math].\overline{0}1[/math] is because some people, in an attempt to refute the fact that [math]1=.\overline{9}[/math], state that [math]1-.\overline{9}=.\overline{0}1[/math], and what dave was trying to show was that [math].\overline{0}1=0[/math], thus showing that [math]1=.\overline{9}[/math]. In fact, the main reason that some people have a problem grasping this equality is that the proof relies heavily upon limits, a tool regularly used in Calculus. In this case, one's intuition runs counter to reality, and thus, a problem arises when people attempt to "intuitively" understand it.

Yeah, that sounds pretty harsh. In the US, it's fairly common for someone to not decide upon their major(s)/minor(s) until their second year of college. I wouldn't be surprised if the concept of a minor was invented so that people who spent 1-2 years in a major could still get some sort of recognition, even though they decided to change majors. Also, it's fairly common for people to change majors as well. So, I assume that a class is associated with each module, and that at the end of each class, the test(s) are administered? Also, on a side note, are classes held year round (with intermittent breaks, of course), or does the UK follow a September - June school year? [joke]The most annoying part of my university education[/joke]. Liberal education requirements are a set of requirements that undergraduates must satisfy regardless of their major. A sample set of requirements would be: 1 introductory Biology course 1 introductory Physics course 1 Mathematics course (usually Calculus I) 2 Social Sciences courses (e.g. History, Political Science) 1 An Art course (e.g. Music, Painting, etc.) There is usually a set of 25-30 classes available to satisfy each individual requirement. Of course, graduate students are not subject to these requirements.

Care to elaborate, pulkit?

Calculus is the name of a particular area of Mathematics, like Algebra, or Geometry, or Analysis. A decent definition of the term "function" is located here http://mathworld.wolfram.com/Function.html

Not at all, please feel free to elaborate. I find the differences rather intriguing. I have a question about your explanation, though. You wrote that So are A-level's scored on an A-F scale? Is this the only information the student will receive about their test, or is a "raw score" provided as well? Forgive my ignorance, but are modules classes, or a series of smaller tests, or something else? So then there is no such thing as "liberal education requirements" that must be satisfied regardless of one's major?

Well' date=' you're supporting the correct result, but with incorrect arguments. To illustrate, let's calculate a couple of values of your series. At [math']n=2[/math] we get [math]10^{-2} \sum_{i=1}^{2} 0\cdot 10^{-i} = 10^{-2}(0 \cdot 10^{-1}+0 \cdot 10^{-2})=0[/math]. At [math]n=3[/math] we get [math]10^{-3} \sum_{i=1}^{3} 0\cdot 10^{-i} = 10^{-3}(0 \cdot 10^{-1}+0 \cdot 10^{-2}+0 \cdot 10^{-3})=0[/math]. Continuing on in this manner, (I omit the inductive argument, for the sake of brevity), one can see that your series always produces [math]0[/math], and not [math]0.\overline{0}1[/math]. I believe what you meant to write was [math]0.\overline{0}1=\lim_{n\to\infty}10^{-n}[/math]. For this expression, at [math]n=1[/math] we get [math]10^{-1}=.1[/math]. At [math]n=2[/math] we get [math]10^{-2}=.01[/math]. At [math]n=3[/math] we get [math]10^{-3}=.001[/math], and so on. Using Calculus, it can be shown that [math]0.\overline{0}1=\lim_{n\to\infty}10^{-n}=0[/math], as desired. As a final note, I would simply like to mention that [math]0.\overline{0}1[/math] is not correct mathematical notation, but the explanation of why would most likely spawn some side debate about [math]\infty[/math], so I'll leave that point unaddressed for now.

Now that you have clarified your point, I find that, for the most part, I agree with your reasoning. Possibly, but I'm sure one could ace an IQ test by doing something that completely defeats the "purpose" of the test, i.e. studying the types of questions that are likely to appear. The problem with this is that such situations do not arise very often in life, and thus, the premise is very hard to test. Also, besides basic sensory-motor skills, at the moment, I cannot think of any "fluid intelligence" (i.e. critical thinking) skills that can only be taught during one's childhood/early developmental stage, so I still contest the above point.

Yes, I believe there is, using Calculus. We wish to maximize [math]x \cdot y[/math] subject to the constraint [math]x+y=n[/math]. Therefore, [math]y=n-x[/math], so our problem is equivalent to maximizing [math]f(x)=x(n-x)=nx-x^2[/math]. Taking the first derivative, (and noting that [math]f(x)[/math] is a downward pointing parabola, and thus, has only one local extrema, a global maximum), we get that [math]f'(x)=n-2x[/math], therefore the local maxima is at [math]x=n/2[/math]. Thus, if [math]x=2k[/math] ([math]k[/math] an integer), the maxima is at [math]x=k[/math], and substituting [math]x[/math] into the constraint equation implies that [math]y=k[/math] as well. However, if [math]n=2k+1[/math], then the maxima is achieved at [math]x = (2k+1)/2=k+1/2[/math], which is not an integer. Therefore, the closest integers are [math]x=k[/math] and [math]x=k+1[/math], which are both a distance of [math]1/2[/math] away from [math]x[/math], and thus, both optimal integer solutions. Again, applying the constraint equation shows that these [math]x[/math]-values correspond to [math]y=k+1[/math] and [math]y=k[/math] respectively. If you have any questions about my explanation, I will gladly expound any requested points.

Would anyone here be willing to give a brief summary of how the pre-collegiate UK (and, if significantly different, the British) education system is structured? Among other topics, I'm interested in the following: when (i.e. what year) students take "standardized" tests, what "A level" tests are, how classes are chosen (primarily by students, or a set schedule, or by some other means), what kind of entrance exams are required before applying to a university, what requirements one needs to satisfy to graduate from various levels, and so on. No summary would have to be formal, for this the purpose of this inquiry is simply to satisfy my curiosity. Also, if anyone is interested, I would be willing to provide a similar summary of the US education system, since that is the system that I have experienced. Finally, I would also be interested in hearing about any other country's educational system, especially if there are some significant differences between its structure, and that of the US.

Nope. The range of a function doesn't have anything to do with "degrees of infinity". As far as I know, the concept of "degrees of infinity" is not a formal mathematical construct. The only concept that I have seen that would fit the "degrees of infinity" description you have supplied is the "big O" notation used in Computer Science classes, which is used to describe the asymptotic behavior of functions. Usually the functions of interest describe the execution time of various algorithms.